890
J. Chem. Eng. Data 1997, 42, 890-893
Thermal Conductivity of Gaseous Trifluoroiodomethane (CF3I) Y. Y. Duan, L. Q. Sun, L. Shi, M. S. Zhu,* and L. Z. Han Thermal Engineering Department, Tsinghua University, Beijing 100084, People’s Republic of China
The thermal conductivity of gaseous trifluoroiodomethane (CF3I) is reported over the temperature range -6.50 °C to 63.55 °C at pressures up to 1000 kPa with an uncertainty of 3% using a transient hot-wire instrument employing two anodized tantalum wires as the heat source. The results were correlated as a function of temperature and density. The values for the thermal conductivity of the dilute gas and the saturated vapor are obtained by extrapolation.
Introduction The traditional refrigerant CFC-12 is widely used in numerous applications. Alternatives of CFC-12 must be developed that are environmentally acceptable and can be used in high-capacity, high-efficiency applications. So far, many CFC alternatives have been developed. HFC-134a has been widely used as a replacement for CFC-12, especially in the United States, Japan, the United Kingdom, and France. But HFC-134a requires physical retrofitting of equipment and does not mix with conventional lubricants. It also has higher global warming potential (GWP) value. Even though they are flammable, hydrocarbons are considered to be another promising alternative, especially in Germany. CF3I has been found to be nonozone depleting, miscible with mineral oil, and compatible with refrigeration system materials. It also has an extremely low GWP value and very low acute toxicity. Therefore, it is also being considered as a promising alternative, especially as a component in mixtures, to replace CFC-12 (Lankford and Nimitz, 1993; Zhao et al., 1995). However, no reliable data for the thermal conductivity of CF3I has been published in recent years. Therefore, research on the thermal conductivity of CF3I is of great interest. This paper reports experimental data for the thermal conductivity of gaseous CF3I in the temperature range from -6.5 to 63.55 °C at pressures up to 1000 kPa with an uncertainty of 3%. Working Equation The theoretical basis of the transient hot-wire technique for gas thermal conductivity measurements has been given in detail elsewhere (Healy et al., 1976). According to the theory, the thermal conductivity, λ, of the fluid can be obtained with the following equations
∆Tid ) ∆Tw +
∑ δT ) 4πλ(T ,F ) lna C q
4kτ
i
r
r
2
(1)
and
Tr ) T0 + 1/2(∆T1 + ∆T2)
(2)
where T0 is the equilibrium temperature of the fluid before heating, Tr is the reference temperature, Fr is the density of the fluid at the reference temperature Tr and the primary pressure p0, q is the energy input per unit length of the hot-wire, τ is the time of heating, a is the wire radius, λ is * To whom correspondence
[email protected].
should
be
addressed.
E-mail:
S0021-9568(97)00037-X CCC: $14.00
the thermal conductivity of the fluid at temperature Tr and pressure p0, ∆Tid is the temperature rise of the hot-wire under the ideal conditions, ∆T1 and ∆T2 are the temperature rises of the hot-wire at the initial moment and the final moment respectively, and C is a numerical constant. The symbol k represents the thermal diffusivity of the fluid surrounding the wires. The various correction terms, δTi, have all been identified (Healy et al., 1976) and are all rendered less than 1% of ∆Tid except the correction term induced by the thermophysical properties of the hot-wire, which is rendered less than 3% of ∆Tid in the interested time range by the design of the wires and the operation of the instrument. It follows from eq 1 that an essential feature of the correct operation of the instrument is that the measured ∆Tid should be a linear function of the logarithm of time, ln τ. Once the temperature rise of the hot-wire is measured as a function of time, τ, the gradient of the linear function of ∆Tid versus the logarithm of τ can be used to calculate the thermal conductivity λ. Instrument The thermal conductivity instrument was described in detail in a previous work (Sun et al., 1997); a modified apparatus is used in this work. The outer part of the instrument is a pressure vessel made of stainless steel which can withstand the pressure of 6 MPa. The inner part which contains the hot-wires is composed of two compartments formed by machining two identical holes centering on the split diameter of a copper cylinder and parallel to its axis. The half of the cylinder shown in Figure 1 carries the five wire supports and is itself supported by the aluminum ring attached to the outer pressure vessel. In this instrument, two 25 µm tantalum wires were used as the hot-wires (13.4 cm and 4.1 cm in length). The wires were anodized in situ to form a layer of insulating tantalum pentoxide on their surface. All electrical connections to the hot-wires were made of 0.8 mm diameter enamel-insulated wire which extends outside of the pressure vessel. The wires were kept vertical and under constant tension by a copper block attached to the bottom of each wire. The mass of the copper blocks was chosen to keep the tension of the hot-wires at 25% of the yielding tension (Menashe and Wakeham, 1981). The wires were connected very carefully to eliminate contact resistance in the measuring system. The instrument employs two hot-wires to eliminate the errors caused by the finite length by using the short wire to compensate for the long wire (Kestin and Wakeham, 1978). The wires were calibrated carefully in situ to determine the resistance temperature coefficient of the tantalum wire. © 1997 American Chemical Society
Journal of Chemical and Engineering Data, Vol. 42, No. 5, 1997 891 Table 1. Measurements of the Thermal Conductivity of N2 P/kPa
Figure 1. Instrument schematic: 1, holes for wire extension; 2, copper block; 3, tested fluid charging hole; 4, mount for wires; 5, gold strip; 6, tantalum wire; 7, copper compartment; 8, pressure vessel; 9, aluminum ring; 10, flange plate.
Figure 2. Unbalanced bridge employed in this work.
The tantalum wire resistance, R(Ω), was represented as a polynomial function of the temperature t, over the temperature range from -10 to 65 °C. A least-squares analysis of the data yielded
t/°C
λlit/mW‚m-1‚ λexp/mW‚ λexp - λlit/mW‚ ((λexp/λlit) K-1 m-1‚K-1 m-1‚K-1 1) × 100
2058.86 23.43
26.814
1702.44 23.36
26.639
1202.85 23.41
26.392
714.84 23.55
26.167
436.00 23.78
26.050
26.778 26.883 26.648 26.611 26.305 26.412 26.080 26.042 25.905 25.831
-0.036 0.069 0.009 -0.028 -0.087 0.020 -0.087 -0.125 -0.145 -0.219
-0.134 0.257 0.034 -0.105 -0.330 0.076 -0.332 -0.478 -0.557 -0.841
bridge measured; R1 and R2 are the resistances of two adjustable resistors, and R3 and R4 are the resistances of two standard fixed resistors. Resistors R1 and R2 were carefully chosen to ensure a uniform energy input, q, into the experiment. The bridge voltage, VE, was measured with a Hewlett Packard 3852A acquisition unit at a collecting rate of about 30 points per s. The temperature rise of the hot-wires was about 3-4 K in the experiment. The instrument uncertainty was estimated less than 3%. The pressure-measurement system included a pistontype pressure gauge, a pressure transducer, and an atmosphere pressure gauge. The accuracy of the piston-type pressure gauge was less than 0.005% in the range 0.1 to 6 MPa. A very sensitive diaphragm pressure transducer (405T) separated the sample from an N2-filled system including the precision piston-type pressure gauge. The accuracy of the transducer was 0.2%, the pressure difference adjustable range was 6 to 38 kPa, the temperature range was 233 to 400 K, and the maximum allowable pressure was 17.8 MPa. The accuracy of the atmospheric pressure gauge was 0.05% over a pressure range of 1 to 160 kPa. The whole pressure measurement system had an uncertainty of (500 Pa. The bath temperature could be varied from 223 to 452 K. The temperature instability was less than (5 mK per 8 h. The overall temperature uncertainty for the bath and temperature-measurement system was less than (10 mK. Results and Analysis
R(t) ) R0[1 + 3.4155 × 10-3(t/°C) - 1.29192 × 10-6(t/°C)2] (3) where R0 represents the resistance of the hot-wires at a temperature of 0 °C. The resistance changes and thus the temperatures rise of the wires were measured by an unbalanced bridge as shown in Figure 2. With this bridge, the difference between the resistance of the two wires can be written in the following form as the two wires are identical except for their length.
∆R ) Rl - Rs )
( )
(4)
R3 VE + V0 R3 + R4
(5)
ll CR1 + CR2 - R1 -1 ls ll (1 - C) - C ls
in which
C)
where Rl is the resistance of the long hot-wire, Rs is the resistance of the short hot-wire, ll is the length of the long wire, ls is the length of the short wire, V0 is the voltage of the power source, VE is the measured voltage across the
Before the thermal conductivity of gaseous CF3I was measured, the thermal conductivity of nitrogen near the isotherm of 23.55 °C was measured and compared with values calculated from an equation recommended in the literature (Stephan et al., 1987). The recommended equation has an accuracy of (0.8%. The measured nitrogen thermal conductivity is listed in Table 1 along with the deviation from the calculated values. The maximum deviation of the measured nitrogen thermal conductivity is less than 1%, and the root mean square deviation is 0.42%. The mass purity of the used nitrogen sample was 99.95%. The thermal conductivity of gaseous CF3I was then measured. The mass purity of the CF3I sample is 99.95%. Figure 3 shows the pressure range and temperature range of the experimental points. Figure 4 shows the temperature rise ∆T versus the logarithm of time τ for a typical run using nitrogen at a bath temperature of 20 °C and a pressure of 436.00 kPa and a typical run using CF3I at a bath temperature of 30 °C and a pressure of 139.93 kPa. The solid line is a linear correlation for CF3I, while the dashed line is a linear correlation for nitrogen. The correlations were determined using a least-squares analysis. There are three parts in the two curves. The first part of each curve is a segment where the thermophysical properties of the hot-wire shows an significant effect and
892 Journal of Chemical and Engineering Data, Vol. 42, No. 5, 1997 Table 2. Thermal Conductivity for CF3I
Figure 3. Temperature and pressure ranges for the experimental points.
t/°C
p/kPa
Fcal/kg‚m-3
λ/mW‚m-1‚K-1
-6.60 -6.50 3.40 3.53 13.50 13.65 13.88 23.79 24.01 24.20 33.70 33.94 34.07 34.20 34.33 43.50 43.70 43.82 43.94 44.06 53.43 53.54 53.66 53.70 53.80 63.25 63.30 63.37 63.45 63.55
147.40 109.56 211.37 136.51 277.63 210.25 103.26 403.76 298.90 225.67 558.50 476.54 357.80 261.25 139.93 615.78 491.57 400.39 276.87 169.43 883.53 677.54 522.99 388.91 243.84 912.58 656.80 537.58 380.88 195.21
13.861 10.125 19.381 12.126 24.776 18.346 8.719 35.629 25.547 18.892 49.031 40.822 29.698 21.176 11.035 52.193 40.369 32.189 21.674 12.980 76.186 55.482 41.392 29.970 18.294 75.123 51.218 40.984 28.252 14.054
6.624 6.594 6.998 6.923 7.402 7.286 7.155 8.026 7.831 7.611 8.623 8.423 8.136 7.956 7.721 9.032 8.745 8.512 8.233 8.034 9.876 9.392 9.034 8.767 8.476 10.123 9.704 9.442 9.123 8.745
Figure 4. Temperature rise of hot-wire and its linear function versus the logarithm of time for both CF3I and nitrogen: (s) CF3I; (- - -) nitrogen.
Figure 6. Thermal conductivity of gaseous CF3I vs density near different isotherms. The temperatures of the isotherms are -6.5 °C, 3.5 °C, 13.6 °C, 24.0 °C, 34.0 °C, 43.8 °C, 53.6 °C, and 63.4 °C, respectively.
Figure 5. Deviation of temperature rise of hot-wire from the correlated linear function for both CF3I and nitrogen: (0) nitrogen; (9) CF3I.
the third part is a segment where natural convection begins to appear and shows a significant effect. The middle part can be described by eqs 1 and 2. Because the thermal conductivity of nitrogen is larger than that of CF3I at corresponding thermodynamic states, the effect of the hotwire thermophysical properties on the measurement for nitrogen can be ignored earlier than CF3I according to the theory of Healy (1976). The relative deviations of the experimentally measured temperature rise from the linear function in Figure 4 are shown in Figure 5 for nitrogen and for CF3I respectively at the thermodynamic states in Figure 4. No curvature or systematic trend is apparent, and the maximum deviation is less than 0.2%. Similar plots were prepared for all the measurements described
in this paper. The lack of any curvature or systematic trend as well as the magnitude of the deviation indicates that no radiation correction is necessary for the temperature range considered (Nieto de Castro et al., 1991). All of the results are given in Table 2. The thermal conductivity data was fit to the following equation using a least-squares analysis 2
λ/mW‚m-1‚K-1 ) a0 + a1(t/°C) + b2(F/kg‚m-3) + 3
4
b3(F/kg‚m-3) + b4(F/kg‚m-3) (6) The coefficients were determined to be: a0 ) 6.661 404, a1 ) 3.018 743 × 10-2, b2 ) 8.299 915 × 10-4, b3 ) -1.074 127 × 10-5, b4 ) 4.509 508 × 10-8. The density of CF3I was calculated by the equation of state provided by Duan et al. (1997). Figure 6 shows the thermal conductivity of CF3I as a function of density near each isotherm, using the vapor pressure equation provided by Duan et al. (1996). Figure 7 shows the deviations of the experimentally measured CF3I thermal conductivity from eq 6, where λexp represents
Journal of Chemical and Engineering Data, Vol. 42, No. 5, 1997 893
λ′′/mW-1‚m-1‚K-1 ) c0 + c1(t/°C) + c2(t/°C)2 + c3(t/°C)3 (7) and
λ0/mW-1‚m-1‚K-1 ) d0 + d1(t/°C)
(8)
The coefficients ci were determined to be c0 ) 6.965 39, c1 ) 4.952 12 × 10-2, c3 ) 5.911 57 × 10-6, and c4 ) 3.835 78 × 10-6. The coefficients di correspond to the coefficients ai in eq 6. Figure 8 shows that λ′′ and λ0 are nearly equal at -10 °C but begin to deviate as temperature increases. This further indicates that both the temperature and density have an obvious effect on the thermal conductivity. Conclusion Figure 7. Deviations of the experimental thermal conductivity from eq 6.
An instrument contained two hot-wires was carefully developed and calibrated for measuring the thermal conductivity of fluids. Nitrogen was used to test the instrument. The thermal conductivity of gaseous CF3I from -6.5 °C to 66.5 °C at pressures up to 1000 kPa with an uncertainty of less than 3% was obtained. Acknowledgment We are indebted to Dr. Nimitz, IKON Co., and Pacific Scientific for providing the CF3I sample. Literature Cited
Figure 8. Curvatures of thermal conductivity for the saturation vapor and the ideal gas of CF3I: (s) curvature for saturation vapor; (- - -) curvature for dilute gas.
the experimental results and λcal are the values calculated from eq 6. The maximum deviation of the experimental results of from eq 6 is 1.1%. The standard deviation of the experimentally measured data from eq 6 is 0.54%. Since eq 6 contains no linear density term, the effect of density on the thermal conductivity is strongly reduced close to the dilute gas state (i.e. F f 0). At this state the density effect should vanish according to the kinetic theory of gases. Equation 6 permits determination of the thermal conductivity of both superheated gas and gas at saturation conditions (solid-line curves in Figure 6). For practical calculations, the thermal conductivities for saturation vapor as well as for the dilute gas (F f 0) are of special interest. The thermal conductivity for these two states are plotted as a function of temperature in Figure 8. The results were extrapolated along isotherms since the density range did not extend to two thermodynamic states. However the density range is wide enough for extrapolation, and the errors caused by extrapolation can be ignored. The thermal conductivity for saturated vapor and for dilute gas, indicated by λ′′ and λ0 respectively, are correlated as
Duan, Y. Y.; Zhu, M. S.; Han, L. Z. Experimental Vapor Pressure Data and a Vapor Pressure Equation for Trifluoroiodomethane (CF3I). Fluid Phase Equilib. 1996, 121, 227-234. Duan, Y. Y.; Zhu, M. S.; Shi, L.; Han, L. Z. Experimental PVT data and an equation of state for trifluoroiodomethane (CF3I) in Gaseous Phase. Fluid Phase Equilib. 1997, in press. Healy, J. J.; De Groot, J. J.; Kestin, J. The Theory of the Transient Hot-wire Method for Measuring Thermal Conductivity. Physica 1976, 82C, 392-408. Kestin, J.; Wakeham, W. A. A Contribution to the Theory of the Transient Hot-wire Technique for Thermal Conductivity Measurements. Physica 1978, 92A, 102-116. Lankford, L.; Nimitz, J. A New Class of High-Performance, Environmentally Sound Refrigerants. Proceedings of the Internation CFC and Halon Alternative Conference, Washington DC, 1993; pp 141149. Menashe, J.; Wakeham, W. A. Absolute Measurements of the Thermal Conductivity of Liquids at Pressures up to 500 MPa. Phys. Chem. 1981, 85, 340-347. Nieto de Castro, C. A.; Perkins, R. A.; Roder, H. M. Radiative Heat Transfer in Transient Hot-wire Measurements of Thermal Conductivity. Int. J. Thermophys. 1991, 12, 985-997. Stephan, K.; Krauss, R.; Laesecke, A. Viscosity and Thermal Conductivity of Nitrogen for a Wide Range of Fluid States. J. Phys. Chem. Ref. Data 1987, 16 (4), 993-1023. Sun, L. Q.; Zhu, M. S.; Han, L. Z.; Lin, Z. Z. Thermal Conductivity of Gaseous Difluoromethane and Pentafluoroethane near the Saturation Line. J. Chem. Eng. Data 1997, 42, 179-182. Zhao, X. Y.; Shi, L.; Zhu, M. S.; Han, L. Z. A New Generation of LongTerm Refrigerants as CFC-12 Alternatives. Proceedings of the International CFC and Halon Alternatives Conference, Washington, DC, 1995; pp 286-293. Received for review February 2, 1997. Accepted May 16, 1997.X This work was supported by the State Education Commission of P.R. China.
JE9700378 X
Abstract published in Advance ACS Abstracts, July 1, 1997.
